This is not an error coming from your template/theme, or from Widgetkit or even your CMS. It's coming from Google as provider of the map service.

Update:
@michael.maas has just published a new tutorial on this subject with some valuable additional information; so, I've deleted the one here, and you may please follow this link here:https://yootheme.com/support/question/100254

*Error in Joomla widgetkit map control panel: map not showing
To show the map on the websie, this is what I did:
1) Find this file:
administrator/components/com_widgetkit/plugins/widgets/map/assets/maps.js

Placing the javascript with API key in the Additional Scripts area of the yootheme template or in the map widget Content area did not work for me, but adding the API key to the administrator/components/com_widgetkit/plugins/widgets/map/assets/maps.js file did work. So far it's the only solution working for me. I realize it's not the ideal solution due to having to re-apply the code after any Widgetkit update. But hopefully the Yootheme dev team will provide a permanent solution with a API key field on the map widget.

I still cannot see the map in the back-end admin of the widget. So I cannot make any map related modifications to the widget at this point.

I´ve had the same problem and was very happy to read your solution here. So I first tried to update my widgekit to 2.7.5
But after this I cann´t reach the frondend of my website anymore. There is no problem with the backend, but using the
frontend-web-adress I get this error message:

is not a statement anyone could help with. Not to mention that it either works, or not at all.

As said in the tutorial (first post), if errors persist, look them up in your browser console, mostly they say what it's about, might even give you a link to Google where you can find more about it and probably also the solution.

Otherwise please open a new thread with all required details - again, as said above.

@michael.maass, thanks for your fast answer 1 day ago. I was wondering, that you´ve been able to reach the side. So I tried to clear the browser-cache, but nothing changed. So I tried other browsers and found out, that only Safari has the problem. Since I was able to reach the site with other browsers, I first thought that the problem had to do in my local Safari installation. However, the phenomenon occurred on other computers with Safari browsers. After a long search I found the cause in the Joomla installation. The plugin "System - Language Filter" caused the error. After I had it turned off the website was back online with Safari.
Greetings from Berlin
Michael

As said in the error and here in the tutorial: Open your browser console to see the exact error.
There will likely be a link to Google's dev pages, where the error is listed and explained. Follow that link, read the error explanations, then do as suggested there.

And as also stated here multiple times, please open a new question for your specific "own" issues. Tutorial threads are not the place for it, for obvious reasons.

I don't understand why existing maps still work on latest Joomla and widgetkit. Do we have to switch to the api or can we leave it as it is?

Only Google could answer this. They are the ones setting the rules for the use of their map (and other) services, and they are the ones deciding when maps on which domain stop working without API key.
Presently, if your map is still working without API key, you'll probably find a warning in your browser console that the API key is missing. As usual, it's a warning and not an error, so for now it still works. As for other domains, at some point in the future the maps may stop working, and an error will then be shown in the console, too. Again, all at Google's discretion.

So, now that you know, it wouldn't hurt to get and use an API key to be prevent sudden errors... wouldn't you agree?